Sharp,
That black wire needs to go to the ring terminal on the jack. If you solder it to the ground terminal you may find your battery will be dead in a few days. The function of the wire is to turn on the active system. It does this by completing the power circuit in the preamp. When you plug your cable in to the jack it shorts the ring to the sleeve and closes the circuit, sending power to whatever needs it, probably a preamp. The tip terminal on the jack conducts the actual "hot" signal to the amp.
So, in review, we have a tip, a ring, and a sleeve. Tip = hot. Ring = battery ground. Sleeve = system ground.
I hope that was clear enough to understand. It's hard to do this without pictures.